Question 232375
First take out a common factor of 2:

{{{2(3x^2 + 14x + 8)}}}


Now, by trial and error, factor this by starting with 3x*x:
{{{2(3x____)(x____) }}}


The Last times Last has to be 8, which is probably going to be 2*4 or 4*2.  The combination that works is 2 *4 like this:

{{{2(3x+2)(x+4){{{   Notice that if you do the OUTER times OUTER you get 3x*4=12x, and the INNER times INNER will be x*2=2x, which adds up to 14x.


{{{2(3x+2)(x+4)}}}


For additional help with this VERY important topic of FACTORING, please visit my own website.  Do a "Bing" or "Google" search for my last name "Rapalje".  Look for "Rapalje Homepage" near the top of the search list.  From my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time."  Select "Basic Algebra" and look in "Chapter 2" for several topics on Factoring, especially "Factoring the Common Factor", "Factoring Trinomials", and "Advanced Trinomial Factoring."  These sections are supported by my "MATH IN LIVING COLOR" pages in which I solved problems IN COLOR!


In addition, I have FREE videos posted of me teaching this topic (a few years ago before I retired!).  To see the videos, from my Homepage, look for "Rapalje Videos in Living Color".  The videos and the non-traditional explanations are all FREE!  I'm not selling anything!!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus